In functional analysis, a branch of mathematics, the Favard operators are defined by:

where , . They are named after Jean Favard.

Generalizations

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A common generalization is:

 

where   is a positive sequence that converges to 0.[1] This reduces to the classical Favard operators when  .

References

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  • Favard, Jean (1944). "Sur les multiplicateurs d'interpolation". Journal de Mathématiques Pures et Appliquées (in French). 23 (9): 219–247. This paper also discussed Szász–Mirakyan operators, which is why Favard is sometimes credited with their development (e.g. Favard–Szász operators).[1]

Footnotes

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  1. ^ Nowak, Grzegorz; Aneta Sikorska-Nowak (14 November 2007). "On the generalized Favard–Kantorovich and Favard–Durrmeyer operators in exponential function spaces". Journal of Inequalities and Applications. 2007: 075142. doi:10.1155/2007/75142.